TY - JOUR
T1 - Maximum principle for non-uniformly parabolic equations and applications
AU - Zhang, Xicheng
N1 - Publisher Copyright:
© 2024 Scuola Normale Superiore. All rights reserved.
PY - 2024
Y1 - 2024
N2 - In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion and drift coefficients. Moreover, by the Markov selection theorem of Krylov [8], we also establish the existence of the associated strong Markov family.
AB - In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion and drift coefficients. Moreover, by the Markov selection theorem of Krylov [8], we also establish the existence of the associated strong Markov family.
UR - http://www.scopus.com/inward/record.url?scp=85167427703&partnerID=8YFLogxK
U2 - 10.2422/2036-2145.202105_052
DO - 10.2422/2036-2145.202105_052
M3 - Article
AN - SCOPUS:85167427703
SN - 0391-173X
VL - 25
SP - 1267
EP - 1308
JO - Annali della Scuola normale superiore di Pisa - Classe di scienze
JF - Annali della Scuola normale superiore di Pisa - Classe di scienze
IS - 3
ER -